The Hardy Space of a Slit Domain

Paperback | August 14, 2009

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The book begins with an exposition of Hardy spaces of slit domains and then proceeds to several descriptions of the invariant subspaces of the operator multiplication by z. Along the way, we discuss and characterize the nearly invariant subspaces of these Hardy spaces and examine conditions for z-invariant subspaces to be cyclic. This work also makes important connections to model spaces for the standard backward shift operator as well as the de Branges spaces of entire functions. The book is written for a graduate student or professional with a reasonable knowledge of Hardy spaces of the disk and basic complex and functional analysis.

From the reviews:"This memoir is concerned with the description of the shift-invariant subspaces of a Hardy space on a slit domain . . this brief monograph represents an interesting and valuable contribution to the literature on the subject of shift-invariant subspaces. It should be helpful for researchers and advanced graduate students specializing in the field." (Dragan Vukotic, Mathematical Reviews, Issue 2011 m)